The Metal Gear Solid series is a sequel to the old MSX/NES Metal Gear series (Metal Gear and Metal Gear 2:Solid Snake). In Metal Gear Solid (Metal Gear Solid:The Twin Snake), they give you a detailed, retconned synopsis of what happened in the original two games. Also, if you have the Metal Gear Solid HD Collection for Xbox 360 or PS3, they include the original 2 games as part of Metal Gear Solid 3. Also, I think some versions of the PS2 game Metal Gear Solid 3 come with them.
To understand the series, you have to play every single game or watch a walk through. The problem is that there is a plot twist like every scene. In fact, after the credits of each of the games, there is a plot twist. The worst of them is in Metal Gear Solid 4 where there is like over an hour's worth of extra scenes after you beat the game that just wraps up the whole series.
Now Metal Gear Solid 2 is a direct sequel to Metal Gear Solid. It is confusing as hell, and you have to figure out towards the end what is really happening and what isn't. Metal Gear Solid 3 is a prequel to the entire Metal Gear series. It introduces some new characters as well as setting up some old characters for the next game, Metal Gear Solid 4.
Metal Gear Solid 4 is divided up into 5 acts. I guarantee this will confuse the heck out of you. It features a lot of characters from the previous games and provides major closure (might make you cry here and there, very emotional, as was Metal Gear Solid 3). At the end of every act, everything you knew before is basically undone by plot twists.
After you beat the game, you think you know everything that has happened, but no. There are more plot twists, credits appear to end but a uber long video sequence wraps things up and more credits roll. You can't skip over anything in this series if you hope to understand the plot. It's that complex.
Now, there are two other games to the Metal Gear Solid Series made for play station portable. It was Metal Gear Solid: Portable Ops and Metal Gear Solid: Peace Walker. They take place after Metal Gear Solid 3 and are meant to be prequels to Metal Gear Solid 4. I never played portable Ops, but Peace Walker includes A LOT of background to the characters of the series and really gives you a better understanding. I can only say so much without spoiling anything. After you beat the game you keep playing and there is even a better REAL ending (the first ending was a fake!) and even after that you can replay old bosses to uncover secret tapes from some of the characters that further reveals more information (this game can be uber sad at time).
Now, there is a sequel for Peace Walker is currently being developed. It's called Metal Gear Solid: Ground Zeroes. The trailer for the game has been released, but no official release date has been set. If you want to catch up on the series, this is where you will end up.
There are plans for one more prequel, to be the sequel to Ground Zeroes, and plans for 2 more Metal Gear Solid games, Metal Gear Solid 5 and Metal Gear Solid 6. They pretty much gave you closure in Metal Gear Solid 4, so I don't know what they're planning for these two game. (EDIT: Metal Gear Solid 5: Phantom Pain takes place between Metal Gear Solid Ground Zeros and Metal Gear). And I haven't mentioned the Metal Gear Rising series. It's a new series that takes place further in the future, but is not needed to under stand the Metal Gear Solid Series.
EDIT: Hideo Kojima, the producer of the Metal Gear Solid series and head honcho of Konami, originally released a 10 minute teaser of Metal Gear Solid: Ground Zeroes to show case his new FOX game engine. He also announced the production of Metal Gear Solid V: Phantom Pain using a fictional production studio (I am not making this up). In March 2013, he revealed that the two games are in fact one in the same and the official trailer was released for Metal Gear Solid V. See the following page for the epic moment: OMG. This is currently where you will end up if you want to catch up on the events of the Metal Gear and Metal Gear Solid series. There should still be a Metal Gear Solid 6 and another possible game after this.
So to summarize, play the games in this order:
- Metal Gear (Optional)
- Metal Gear 2: Solid Snake (Optional)
- Metal Gear Solid/Metal Gear Solid:The twin snakes (Read retconned Metal Gear and Metal Gear 2:Solid Snake synopsis first)
- Metal Gear Solid 2:Sons of Libery
- Metal Gear Solid 3:Snake Eater
- Metal Gear Solid 4:Guns of the Patriots
- Metal Gear Solid: Portable Ops
- Metal Gear Solid: Peace Walker (needed if you want to play MGSV)
- Metal Gear Solid: Ground Zeroes/Metal Gear Solid 5: Phantom Pain (Not sure when it will be released)
- Unnamed Metal Gear game (not to sure about this)
- Metal Gear Solid 6 (this is suppose to be the end of the series...)